Question: Solve for $x$ and $y$ using elimination. ${-6x+4y = -8}$ ${5x+2y = 12}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${-6x+4y = -8}$ $-10x-4y = -24$ Add the top and bottom equations together. $-16x = -32$ $\dfrac{-16x}{{-16}} = \dfrac{-32}{{-16}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-6x+4y = -8}\thinspace$ to find $y$ ${-6}{(2)}{ + 4y = -8}$ $-12+4y = -8$ $-12{+12} + 4y = -8{+12}$ $4y = 4$ $\dfrac{4y}{{4}} = \dfrac{4}{{4}}$ ${y = 1}$ You can also plug ${x = 2}$ into $\thinspace {5x+2y = 12}\thinspace$ and get the same answer for $y$ : ${5}{(2)}{ + 2y = 12}$ ${y = 1}$